Creating a function f_dargN for each possible N is no longer necessary

[efremale]

Calling clad::differentiate(f, N) for 0 <= N <= M and T f(T x0, ..., T xM) currently would produce M+1 derivative functions f_dargN that are very similar. In fact, they only differ in how the initial derivatives of function parameters are initialized:

T f_dargN(T x0, ..., T xM) {
  ...
  T _d_xN = 1;
  T _d_xI = 0; // for all I != N
  ...
  // common code part here
}

We can perhaps utilize it and create only one function, where initial derivatives are specified by a caller:

T f_darg(T x0, T _d_x0, ..., T xM, T _d_xM)

This would allow the caller to specify the independent variable by passing the required _d_xI equal to 1.
This is also potentially useful for deriving functions with vector inputs as each vector input has its derivative specified by a user and we no longer have to allocate it.

[vaithak]

This was fixed in #565 and many subsequent PRs which added the vector forward mode support.

We also have many test cases present with the vector mode interface: https://github.com/vgvassilev/clad/blob/master/test/ForwardMode/VectorMode.C.
Demo example: https://github.com/vgvassilev/clad/blob/master/demos/VectorForwardMode.cpp

[vgvassilev]

Thanks @vaithak, let's close the issue now.